共查询到20条相似文献,搜索用时 15 毫秒
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This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier–Stokes equations coupled with an evolutionary equation for the magnetization vector and the Cahn–Hilliard equations. We show global in time existence of weak solutions to the system using the time discretization method. 相似文献
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Xuguang Lu 《Journal of Differential Equations》2008,245(7):1705-1761
For general initial data we prove the global existence and weak stability of weak solutions of the Boltzmann equation for Fermi-Dirac particles in a periodic box for very soft potentials (−5<γ?−3) with a weak angular cutoff. In particular the Coulomb interaction (γ=−3) with the weak angular cutoff is included. The conservation of energy and moment estimates are also proven under a further angular cutoff. The proof is based on the entropy inequality, velocity averaging compactness of weak solutions, and various continuity properties of general Boltzmann collision integral operators. 相似文献
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The authors discuss the quasilinear parabolic equation ut=∇⋅(g(u)∇u)+h(u,∇u)+f(u) with u|∂Ω=0, u(x,0)=?(x). If f, g and h are polynomials with proper degrees and proper coefficients, they show that the blowup property only depends on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For a special case, they obtain a sharp result. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(6):1271-1297
In this paper, we study the problem of global existence of weak solutions for the quasi-stationary compressible Stokes equations with an anisotropic viscous tensor. The key idea is a new identity that we obtain by comparing the limit of the equations of the energies associated to a sequence of weak-solutions with the energy equation associated to the system verified by the limit of the sequence of weak-solutions. In the context of stability of weak solutions, this allows us to construct a defect measure which is used to prove compactness for the density and therefore allowing us to identify the pressure in the limiting model. By doing so we avoid the use of the so-called effective flux. Using this new tool, we solve an open problem namely global existence of solutions à la Leray for such a system without assuming any restriction on the anisotropy amplitude. This provides a flexible and natural method to treat compressible quasilinear Stokes systems which are important for instance in biology, porous media, supra-conductivity or other applications in the low Reynolds number regime. 相似文献
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Yaojun Ye 《Applicable analysis》2017,96(16):2869-2890
The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given. 相似文献
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In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution. 相似文献
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Chunxia Guan 《Journal of Functional Analysis》2011,260(4):1132-2159
In this paper, we prove the existence of global weak solution for an integrable two-component Camassa-Holm shallow water system provided the initial data satisfying some certain conditions. 相似文献
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Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source 总被引:1,自引:0,他引:1
In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions gi(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property. 相似文献
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This paper is concerned with global existence and exponential stability of solutions for a class of full non-Newtonian fluids with large initial data in a bounded domain Ω?(0,1). 相似文献
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Consider a quasi-linear system of two Klein-Gordon equations with masses m1, m2. We prove that when m1≠2m2 and m2≠2m1, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308) in the semi-linear case. Moreover, we show that global existence holds true also when m1=2m2 and a convenient null condition is satisfied by the nonlinearities. 相似文献
12.
Nadia Mezouar 《Applicable analysis》2020,99(10):1724-1748
ABSTRACT In this paper, a nonlinear viscoelastic kirchhoff equation in a bounded domain with a time varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo–Galarkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. 相似文献
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Global existence and blow-up solutions for doubly degenerate parabolic system with nonlocal source 总被引:1,自引:0,他引:1
Jian Wang 《Journal of Mathematical Analysis and Applications》2011,374(1):290-310
This paper deals with the following nonlocal doubly degenerate parabolic system
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Tatsuki Kawakami 《Journal of Mathematical Analysis and Applications》2010,368(1):320-329
We consider the initial-boundary value problem for the heat equation with a nonlinear boundary condition:
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In this paper, we prove that the global existence of classical solutions to the Cauchy problem for the minimal surface equation with slow decay initial value in Minkowskian space time. 相似文献
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Shaohua Chen 《Journal of Differential Equations》2008,245(4):1112-1136
The author discusses the degenerate and quasilinear parabolic system